03043nam 2200565 450 991082743390332120170918221534.01-4704-0748-5(CKB)3360000000464518(EBL)3113821(SSID)ssj0000889223(PQKBManifestationID)11523075(PQKBTitleCode)TC0000889223(PQKBWorkID)10876215(PQKB)11536521(MiAaPQ)EBC3113821(RPAM)4278560(PPN)195412168(EXLCZ)99336000000046451820140903h19851985 uy 0engur|n|---|||||txtccrThe spectral theory of geometrically periodic hyperbolic 3-manifolds /Charles L. EpsteinProvidence, Rhode Island :American Mathematical Society,1985.©19851 online resource (174 p.)Memoirs of the American Mathematical Society,0065-9266 ;Volume 58, Numbr 335"November 1985, volume 58 number 335 (first of four numbers)."0-8218-2336-1 Includes bibliographical references.""Table of Contents""; ""Notation""; ""1. Preliminaries""; ""1.1 Introduction""; ""1.2 Holomorphic Families of Operators""; ""2. Floquet Theory""; ""2.1 An Equivalent Family of Operators""; ""2.2 A Second Equivalent Family of Operators""; ""3. The Elliptic Case""; ""3.1 The Analyticity of the Operators""; ""3.2 An Estimate on the Derivatives of the Eigenvalues""; ""3.3 A Lower Bound on the Density of the Absolutely Continuous Spectrum""; ""3.4 The Structure of the Spectrum Near Zero""; ""4. The Parabolic Case""; ""4.1 Introduction""; ""4.2 The Analyticity of L[sub(Î?)]""""4.3 Boundary Behavior of L[sub(Î?)]""""4.4 The Absolutely Continuous Spectrum of -Î? on H[sup(3)]/Î?""; ""4.5 The Asymptotic Behavior of λ[sub(1)](Î?) Near Zero""; ""5. Applications of the Spectral Theory""; ""5.1 Introduction""; ""5.2 The L[sup(2)] Theory of the Wave Equation in H[sup(3)]/Î?""; ""5.3 Lattice Point Asymptotics: The Exact Leading Order Term""; ""5.4 The Explicit Leading Term for â??(R)""; ""5.5 Asymptotics of the Lengths of Closed Geodesies""; ""Appendices""; ""1. Hyperbolic Manifolds and Hyperbolic Isometries""; ""2. A Uniform Estimate for K[sub(Ï?)](z)""""3. Derivation of a Selberg Trace Formula""""References""Memoirs of the American Mathematical Society ;Volume 58, Numbr 335.Three-manifolds (Topology)Spectral theory (Mathematics)Three-manifolds (Topology)Spectral theory (Mathematics)514/.7Epstein Charles L.94497MiAaPQMiAaPQMiAaPQBOOK9910827433903321The spectral theory of geometrically periodic hyperbolic 3-manifolds4113789UNINA